Coloring the 600 Cell
Abstract
The 600 cell S has exactly 10 5-colorings. From these colorings we can construct the space of colorings B(S). This complex has 1344 colorings, and is isomorphic to the space of 5 by 5 Latin Squares. These simplices split into 4 copies of a quotient of S by an involution, and two copies of a space made up of even Latin Squares.
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